The Obama administration has been under fire for initially linking the attack on the compound to an anti-Islam video made in the U.S. before later acknowledging that that the attack was an act of terrorism, not a protest that turned violent.

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Graham, speaking on CBS, said the attack undercuts a “narrative” the administration has been peddling about dismantling al-Qaeda and foreign policy successes in the Middle East. “I think they have been misleading us but it finally caught up with them,” he said on "Face the Nation."

“Either they are misleading the American people or incredibly incompetent. There is no way, with anybody looking at all, that you could believe five days after the attack it was based on a riot that never occurred,” he said.

Republicans, in particular, have blasted U.S. Ambassador to the United Nations Susan Rice for accounts of the Sept. 11, 2012 attack that she gave on the Sunday news shows on Sept. 16.

White House officials have said their shifting account was based on new information coming to light from the intelligence community.

But Graham said intelligence officials quickly knew that it was a terrorist attack.

“The intelligence community on the ground in Libya has told Sen. [Bob] Corker [R-Tenn.] and myself that within 24 hours they communicated up to Washington that this was a terrorist attack,” said Graham.